I thought the origins of Syphilis was more conclusive than the above post by Mindy suggests. Mae Culpa if it didn’t originate in the New Word. IIRC I got his nugget from someone citing Guns, Germs, and Steel - but I haven’t finished reading that actual book.
As for KNOWINGLY giving the Natives of the New World diseases: Early on they didn’t know how the various diseases were spread and the original interaction that is estimated to have wiped out 80-90% of the native population, just spreading how diseases do.
There is evidence of one British officer in the 1700s saying they gave a couple blankets away, and another letter of a British general musing the idea of using tainted blankets. But there is no evidence this was something done in a widespread fashion. The vast majority it is believed came into contact through “normal means”, and unfortunately with zero immunity the death tolls were incredibly high.
As I mentioned above, the New World had nearly no domesticated animals, and thus unlike Africa, Europe or Asia, they didn’t have a ton of people living near animals. Most of the plagues and epidemic diseases like Small Pox jumped from animals to humans. Thus they had more plagues and had more time to build up some immunity to them. This whole world and especially the US would look A LOT different if we just had some Cows or Oxen or Horses in the New World.